Daily Papers

Text-driven controllable dance generation remains under-explored, primarily due to the severe scarcity of high-quality datasets and the inherent difficulty of articulating complex choreographies. Characterizing dance is particularly challenging owing to its intricate spatial dynamics, strong directionality, and the highly decoupled movements of distinct body parts. To overcome these bottlenecks, we bridge principles from dance studies, human anatomy, and biomechanics to propose Choreographic Syntax, a novel theoretical framework with a tailored annotation system. Grounded in this syntax, we combine professional dance archives with high-fidelity motion capture data to construct DanceFlow, the most fine-grained dance dataset to date. It encompasses 41 hours of high-quality motions paired with 6.34 million words of detailed descriptions. At the model level, we introduce DanceCrafter, a tailored motion transformer built upon the Momentum Human Rig. To circumvent optimization instabilities, we construct a continuous manifold motion representation paired with a hybrid normalization strategy. Furthermore, we design an anatomy-aware loss to explicitly regulate the decoupled nature of body parts. Together, these adaptations empower DanceCrafter to achieve the high-fidelity and stable generation of complex dance sequences. Extensive evaluations and user studies demonstrate our state-of-the-art performance in motion quality, fine-grained controllability, and generation naturalness.

In neural networks, it is often desirable to work with various representations of the same space. For example, 3D rotations can be represented with quaternions or Euler angles. In this paper, we advance a definition of a continuous representation, which can be helpful for training deep neural networks. We relate this to topological concepts such as homeomorphism and embedding. We then investigate what are continuous and discontinuous representations for 2D, 3D, and n-dimensional rotations. We demonstrate that for 3D rotations, all representations are discontinuous in the real Euclidean spaces of four or fewer dimensions. Thus, widely used representations such as quaternions and Euler angles are discontinuous and difficult for neural networks to learn. We show that the 3D rotations have continuous representations in 5D and 6D, which are more suitable for learning. We also present continuous representations for the general case of the n-dimensional rotation group SO(n). While our main focus is on rotations, we also show that our constructions apply to other groups such as the orthogonal group and similarity transforms. We finally present empirical results, which show that our continuous rotation representations outperform discontinuous ones for several practical problems in graphics and vision, including a simple autoencoder sanity test, a rotation estimator for 3D point clouds, and an inverse kinematics solver for 3D human poses.

We present a new approach for understanding the periodicity structure and semantics of motion datasets, independently of the morphology and skeletal structure of characters. Unlike existing methods using an overly sparse high-dimensional latent, we propose a phase manifold consisting of multiple closed curves, each corresponding to a latent amplitude. With our proposed vector quantized periodic autoencoder, we learn a shared phase manifold for multiple characters, such as a human and a dog, without any supervision. This is achieved by exploiting the discrete structure and a shallow network as bottlenecks, such that semantically similar motions are clustered into the same curve of the manifold, and the motions within the same component are aligned temporally by the phase variable. In combination with an improved motion matching framework, we demonstrate the manifold's capability of timing and semantics alignment in several applications, including motion retrieval, transfer and stylization. Code and pre-trained models for this paper are available at https://peizhuoli.github.io/walkthedog.

In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both SO(3)timesR^3 and SE(3) pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to achieve the best model for the ME task. In addition, unique to our framework, we derive the kinematic models with the closed-form temporal derivatives of the local variable of SO(3) and SE(3), which so far has only been approximated based on the Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available at https://github.com/brytsknguyen/gptr.

Human motion generation is often learned in Euclidean spaces, although valid motions follow structured non-Euclidean geometry. We present Riemannian Motion Generation (RMG), a unified framework that represents motion on a product manifold and learns dynamics via Riemannian flow matching. RMG factorizes motion into several manifold factors, yielding a scale-free representation with intrinsic normalization, and uses geodesic interpolation, tangent-space supervision, and manifold-preserving ODE integration for training and sampling. On HumanML3D, RMG achieves state-of-the-art FID in the HumanML3D format (0.043) and ranks first on all reported metrics under the MotionStreamer format. On MotionMillion, it also surpasses strong baselines (FID 5.6, R@1 0.86). Ablations show that the compact T+R (translation + rotations) representation is the most stable and effective, highlighting geometry-aware modeling as a practical and scalable route to high-fidelity motion generation.

Video representation is a long-standing problem that is crucial for various down-stream tasks, such as tracking,depth prediction,segmentation,view synthesis,and editing. However, current methods either struggle to model complex motions due to the absence of 3D structure or rely on implicit 3D representations that are ill-suited for manipulation tasks. To address these challenges, we introduce a novel explicit 3D representation-video Gaussian representation -- that embeds a video into 3D Gaussians. Our proposed representation models video appearance in a 3D canonical space using explicit Gaussians as proxies and associates each Gaussian with 3D motions for video motion. This approach offers a more intrinsic and explicit representation than layered atlas or volumetric pixel matrices. To obtain such a representation, we distill 2D priors, such as optical flow and depth, from foundation models to regularize learning in this ill-posed setting. Extensive applications demonstrate the versatility of our new video representation. It has been proven effective in numerous video processing tasks, including tracking, consistent video depth and feature refinement, motion and appearance editing, and stereoscopic video generation. Project page: https://sunyangtian.github.io/spatter_a_video_web/

Human motion, inherently continuous and dynamic, presents significant challenges for generative models. Despite their dominance, discrete quantization methods, such as VQ-VAEs, suffer from inherent limitations, including restricted expressiveness and frame-wise noise artifacts. Continuous approaches, while producing smoother and more natural motions, often falter due to high-dimensional complexity and limited training data. To resolve this "discord" between discrete and continuous representations, we introduce DisCoRD: Discrete Tokens to Continuous Motion via Rectified Flow Decoding, a novel method that decodes discrete motion tokens into continuous motion through rectified flow. By employing an iterative refinement process in the continuous space, DisCoRD captures fine-grained dynamics and ensures smoother and more natural motions. Compatible with any discrete-based framework, our method enhances naturalness without compromising faithfulness to the conditioning signals. Extensive evaluations demonstrate that DisCoRD achieves state-of-the-art performance, with FID of 0.032 on HumanML3D and 0.169 on KIT-ML. These results solidify DisCoRD as a robust solution for bridging the divide between discrete efficiency and continuous realism. Our project page is available at: https://whwjdqls.github.io/discord.github.io/.

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on many real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries.

We propose novel motion representations for animating articulated objects consisting of distinct parts. In a completely unsupervised manner, our method identifies object parts, tracks them in a driving video, and infers their motions by considering their principal axes. In contrast to the previous keypoint-based works, our method extracts meaningful and consistent regions, describing locations, shape, and pose. The regions correspond to semantically relevant and distinct object parts, that are more easily detected in frames of the driving video. To force decoupling of foreground from background, we model non-object related global motion with an additional affine transformation. To facilitate animation and prevent the leakage of the shape of the driving object, we disentangle shape and pose of objects in the region space. Our model can animate a variety of objects, surpassing previous methods by a large margin on existing benchmarks. We present a challenging new benchmark with high-resolution videos and show that the improvement is particularly pronounced when articulated objects are considered, reaching 96.6% user preference vs. the state of the art.

As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous representation for meshes with fixed topology, a common and practical setting in many faces-, hand-, and body-related applications. First, we split the template into multiple closed manifold genus-0 meshes so that each genus-0 mesh can be parameterized onto the unit sphere. Then we learn spherical implicit surface (SIS), which takes a spherical coordinate and a global feature or a set of local features around the coordinate as inputs, predicting the vertex corresponding to the coordinate as an output. Since the spherical coordinates are continuous, SIS can depict a mesh in an arbitrary resolution. SIS representation builds a bridge between discrete and continuous representation in 3D shapes. Specifically, we train SIS networks in a self-supervised manner for two tasks: a reconstruction task and a super-resolution task. Experiments show that our SIS representation is comparable with state-of-the-art methods that are specifically designed for meshes with a fixed resolution and significantly outperforms methods that work in arbitrary resolutions.

We consider the problem of segmenting objects in videos based on their motion and no other forms of supervision. Prior work has often approached this problem by using the principle of common fate, namely the fact that the motion of points that belong to the same object is strongly correlated. However, most authors have only considered instantaneous motion from optical flow. In this work, we present a way to train a segmentation network using long-term point trajectories as a supervisory signal to complement optical flow. The key difficulty is that long-term motion, unlike instantaneous motion, is difficult to model -- any parametric approximation is unlikely to capture complex motion patterns over long periods of time. We instead draw inspiration from subspace clustering approaches, proposing a loss function that seeks to group the trajectories into low-rank matrices where the motion of object points can be approximately explained as a linear combination of other point tracks. Our method outperforms the prior art on motion-based segmentation, which shows the utility of long-term motion and the effectiveness of our formulation.

Since 2023, Vector Quantization (VQ)-based discrete generation methods have rapidly dominated human motion generation, primarily surpassing diffusion-based continuous generation methods in standard performance metrics. However, VQ-based methods have inherent limitations. Representing continuous motion data as limited discrete tokens leads to inevitable information loss, reduces the diversity of generated motions, and restricts their ability to function effectively as motion priors or generation guidance. In contrast, the continuous space generation nature of diffusion-based methods makes them well-suited to address these limitations and with even potential for model scalability. In this work, we systematically investigate why current VQ-based methods perform well and explore the limitations of existing diffusion-based methods from the perspective of motion data representation and distribution. Drawing on these insights, we preserve the inherent strengths of a diffusion-based human motion generation model and gradually optimize it with inspiration from VQ-based approaches. Our approach introduces a human motion diffusion model enabled to perform bidirectional masked autoregression, optimized with a reformed data representation and distribution. Additionally, we also propose more robust evaluation methods to fairly assess different-based methods. Extensive experiments on benchmark human motion generation datasets demonstrate that our method excels previous methods and achieves state-of-the-art performances.

In this paper, we adopt the Universal Manifold Embedding (UME) framework for the estimation of rigid transformations and extend it, so that it can accommodate scenarios involving partial overlap and differently sampled point clouds. UME is a methodology designed for mapping observations of the same object, related by rigid transformations, into a single low-dimensional linear subspace. This process yields a transformation-invariant representation of the observations, with its matrix form representation being covariant (i.e. equivariant) with the transformation. We extend the UME framework by introducing a UME-compatible feature extraction method augmented with a unique UME contrastive loss and a sampling equalizer. These components are integrated into a comprehensive and robust registration pipeline, named UMERegRobust. We propose the RotKITTI registration benchmark, specifically tailored to evaluate registration methods for scenarios involving large rotations. UMERegRobust achieves better than state-of-the-art performance on the KITTI benchmark, especially when strict precision of (1{\deg}, 10cm) is considered (with an average gain of +9%), and notably outperform SOTA methods on the RotKITTI benchmark (with +45% gain compared the most recent SOTA method).

This paper addresses the challenge of reconstructing dynamic 3D scenes with complex motions. Some recent works define 3D Gaussian primitives in the canonical space and use deformation fields to map canonical primitives to observation spaces, achieving real-time dynamic view synthesis. However, these methods often struggle to handle scenes with complex motions due to the difficulty of optimizing deformation fields. To overcome this problem, we propose FreeTimeGS, a novel 4D representation that allows Gaussian primitives to appear at arbitrary time and locations. In contrast to canonical Gaussian primitives, our representation possesses the strong flexibility, thus improving the ability to model dynamic 3D scenes. In addition, we endow each Gaussian primitive with an motion function, allowing it to move to neighboring regions over time, which reduces the temporal redundancy. Experiments results on several datasets show that the rendering quality of our method outperforms recent methods by a large margin.

Recent techniques for text-to-4D generation synthesize dynamic 3D scenes using supervision from pre-trained text-to-video models. However, existing representations for motion, such as deformation models or time-dependent neural representations, are limited in the amount of motion they can generate-they cannot synthesize motion extending far beyond the bounding box used for volume rendering. The lack of a more flexible motion model contributes to the gap in realism between 4D generation methods and recent, near-photorealistic video generation models. Here, we propose TC4D: trajectory-conditioned text-to-4D generation, which factors motion into global and local components. We represent the global motion of a scene's bounding box using rigid transformation along a trajectory parameterized by a spline. We learn local deformations that conform to the global trajectory using supervision from a text-to-video model. Our approach enables the synthesis of scenes animated along arbitrary trajectories, compositional scene generation, and significant improvements to the realism and amount of generated motion, which we evaluate qualitatively and through a user study. Video results can be viewed on our website: https://sherwinbahmani.github.io/tc4d.

Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv

We present an unsupervised representation learning approach that compactly encodes the motion dependencies in videos. Given a pair of images from a video clip, our framework learns to predict the long-term 3D motions. To reduce the complexity of the learning framework, we propose to describe the motion as a sequence of atomic 3D flows computed with RGB-D modality. We use a Recurrent Neural Network based Encoder-Decoder framework to predict these sequences of flows. We argue that in order for the decoder to reconstruct these sequences, the encoder must learn a robust video representation that captures long-term motion dependencies and spatial-temporal relations. We demonstrate the effectiveness of our learned temporal representations on activity classification across multiple modalities and datasets such as NTU RGB+D and MSR Daily Activity 3D. Our framework is generic to any input modality, i.e., RGB, Depth, and RGB-D videos.

We present Motion 3-to-4, a feed-forward framework for synthesising high-quality 4D dynamic objects from a single monocular video and an optional 3D reference mesh. While recent advances have significantly improved 2D, video, and 3D content generation, 4D synthesis remains difficult due to limited training data and the inherent ambiguity of recovering geometry and motion from a monocular viewpoint. Motion 3-to-4 addresses these challenges by decomposing 4D synthesis into static 3D shape generation and motion reconstruction. Using a canonical reference mesh, our model learns a compact motion latent representation and predicts per-frame vertex trajectories to recover complete, temporally coherent geometry. A scalable frame-wise transformer further enables robustness to varying sequence lengths. Evaluations on both standard benchmarks and a new dataset with accurate ground-truth geometry show that Motion 3-to-4 delivers superior fidelity and spatial consistency compared to prior work. Project page is available at https://motion3-to-4.github.io/.

We present a new test-time optimization method for estimating dense and long-range motion from a video sequence. Prior optical flow or particle video tracking algorithms typically operate within limited temporal windows, struggling to track through occlusions and maintain global consistency of estimated motion trajectories. We propose a complete and globally consistent motion representation, dubbed OmniMotion, that allows for accurate, full-length motion estimation of every pixel in a video. OmniMotion represents a video using a quasi-3D canonical volume and performs pixel-wise tracking via bijections between local and canonical space. This representation allows us to ensure global consistency, track through occlusions, and model any combination of camera and object motion. Extensive evaluations on the TAP-Vid benchmark and real-world footage show that our approach outperforms prior state-of-the-art methods by a large margin both quantitatively and qualitatively. See our project page for more results: http://omnimotion.github.io/

Enhancing low-resolution, low-frame-rate videos to high-resolution, high-frame-rate quality is essential for a seamless user experience, motivating advancements in Continuous Spatial-Temporal Video Super Resolution (C-STVSR). While prior methods employ Implicit Neural Representation (INR) for continuous encoding, they often struggle to capture the complexity of video data, relying on simple coordinate concatenation and pre-trained optical flow network for motion representation. Interestingly, we find that adding position encoding, contrary to common observations, does not improve-and even degrade performance. This issue becomes particularly pronounced when combined with pre-trained optical flow networks, which can limit the model's flexibility. To address these issues, we propose BF-STVSR, a C-STVSR framework with two key modules tailored to better represent spatial and temporal characteristics of video: 1) B-spline Mapper for smooth temporal interpolation, and 2) Fourier Mapper for capturing dominant spatial frequencies. Our approach achieves state-of-the-art PSNR and SSIM performance, showing enhanced spatial details and natural temporal consistency.

Recent work in unsupervised multi-object segmentation shows impressive results by predicting motion from a single image despite the inherent ambiguity in predicting motion without the next image. On the other hand, the set of possible motions for an image can be constrained to a low-dimensional space by considering the scene structure and moving objects in it. We propose to model pixel-wise geometry and object motion to remove ambiguity in reconstructing flow from a single image. Specifically, we divide the image into coherently moving regions and use depth to construct flow bases that best explain the observed flow in each region. We achieve state-of-the-art results in unsupervised multi-object segmentation on synthetic and real-world datasets by modeling the scene structure and object motion. Our evaluation of the predicted depth maps shows reliable performance in monocular depth estimation.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

Articulated objects are common in the real world, yet modeling their structure and motion remains a challenging task for 3D reconstruction methods. In this work, we introduce Part^{2}GS, a novel framework for modeling articulated digital twins of multi-part objects with high-fidelity geometry and physically consistent articulation. Part^{2}GS leverages a part-aware 3D Gaussian representation that encodes articulated components with learnable attributes, enabling structured, disentangled transformations that preserve high-fidelity geometry. To ensure physically consistent motion, we propose a motion-aware canonical representation guided by physics-based constraints, including contact enforcement, velocity consistency, and vector-field alignment. Furthermore, we introduce a field of repel points to prevent part collisions and maintain stable articulation paths, significantly improving motion coherence over baselines. Extensive evaluations on both synthetic and real-world datasets show that Part^{2}GS consistently outperforms state-of-the-art methods by up to 10times in Chamfer Distance for movable parts.

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

Conditional human motion generation is an important topic with many applications in virtual reality, gaming, and robotics. While prior works have focused on generating motion guided by text, music, or scenes, these typically result in isolated motions confined to short durations. Instead, we address the generation of long, continuous sequences guided by a series of varying textual descriptions. In this context, we introduce FlowMDM, the first diffusion-based model that generates seamless Human Motion Compositions (HMC) without any postprocessing or redundant denoising steps. For this, we introduce the Blended Positional Encodings, a technique that leverages both absolute and relative positional encodings in the denoising chain. More specifically, global motion coherence is recovered at the absolute stage, whereas smooth and realistic transitions are built at the relative stage. As a result, we achieve state-of-the-art results in terms of accuracy, realism, and smoothness on the Babel and HumanML3D datasets. FlowMDM excels when trained with only a single description per motion sequence thanks to its Pose-Centric Cross-ATtention, which makes it robust against varying text descriptions at inference time. Finally, to address the limitations of existing HMC metrics, we propose two new metrics: the Peak Jerk and the Area Under the Jerk, to detect abrupt transitions.

Unsupervised learning of depth and ego-motion, two fundamental 3D perception tasks, has made significant strides in recent years. However, most methods treat ego-motion as an auxiliary task, either mixing all motion types or excluding depth-independent rotational motions in supervision. Such designs limit the incorporation of strong geometric constraints, reducing reliability and robustness under diverse conditions. This study introduces a discriminative treatment of motion components, leveraging the geometric regularities of their respective rigid flows to benefit both depth and ego-motion estimation. Given consecutive video frames, network outputs first align the optical axes and imaging planes of the source and target cameras. Optical flows between frames are transformed through these alignments, and deviations are quantified to impose geometric constraints individually on each ego-motion component, enabling more targeted refinement. These alignments further reformulate the joint learning process into coaxial and coplanar forms, where depth and each translation component can be mutually derived through closed-form geometric relationships, introducing complementary constraints that improve depth robustness. DiMoDE, a general depth and ego-motion joint learning framework incorporating these designs, achieves state-of-the-art performance on multiple public datasets and a newly collected diverse real-world dataset, particularly under challenging conditions. Our source code will be publicly available at mias.group/DiMoDE upon publication.

Nonlinear manifolds are widespread in deep visual features, where Euclidean distances often fail to capture true similarity. This limitation becomes particularly severe in prototype-based interpretable fine-grained recognition, where subtle semantic distinctions are essential. To address this challenge, we propose a novel paradigm for prototype-based recognition that anchors similarity within the intrinsic geometry of deep features. Specifically, we distill the latent manifold structure of each class into a diffusion space and introduce a differentiable Nystr\"om interpolation, making the geometry accessible to both unseen samples and learnable prototypes. To ensure efficiency, we employ compact per-class landmark sets with periodic updates. This design keeps the embedding aligned with the evolving backbone, enabling fast and scalable inference. Extensive experiments on the CUB-200-2011 and Stanford Cars datasets show that our GeoProto framework produces prototypes focusing on semantically aligned parts, significantly outperforming Euclidean prototype networks.

Monocular dynamic reconstruction is a challenging and long-standing vision problem due to the highly ill-posed nature of the task. Existing approaches are limited in that they either depend on templates, are effective only in quasi-static scenes, or fail to model 3D motion explicitly. In this work, we introduce a method capable of reconstructing generic dynamic scenes, featuring explicit, full-sequence-long 3D motion, from casually captured monocular videos. We tackle the under-constrained nature of the problem with two key insights: First, we exploit the low-dimensional structure of 3D motion by representing scene motion with a compact set of SE3 motion bases. Each point's motion is expressed as a linear combination of these bases, facilitating soft decomposition of the scene into multiple rigidly-moving groups. Second, we utilize a comprehensive set of data-driven priors, including monocular depth maps and long-range 2D tracks, and devise a method to effectively consolidate these noisy supervisory signals, resulting in a globally consistent representation of the dynamic scene. Experiments show that our method achieves state-of-the-art performance for both long-range 3D/2D motion estimation and novel view synthesis on dynamic scenes. Project Page: https://shape-of-motion.github.io/

With diffusion and flow matching models achieving state-of-the-art generating performance, the interest of the community now turned to reducing the inference time without sacrificing sample quality. Consistency Models (CMs), which are trained to be consistent on diffusion or probability flow ordinary differential equation (PF-ODE) trajectories, enable one or two-step flow or diffusion sampling. However, CMs typically require prolonged training with large batch sizes to obtain competitive sample quality. In this paper, we examine the training dynamics of CMs near convergence and discover that CM tangents -- CM output update directions -- are quite oscillatory, in the sense that they move parallel to the data manifold, not towards the manifold. To mitigate oscillatory tangents, we propose a new loss function, called the manifold feature distance (MFD), which provides manifold-aligned tangents that point toward the data manifold. Consequently, our method -- dubbed Align Your Tangent (AYT) -- can accelerate CM training by orders of magnitude and even out-perform the learned perceptual image patch similarity metric (LPIPS). Furthermore, we find that our loss enables training with extremely small batch sizes without compromising sample quality. Code: https://github.com/1202kbs/AYT

Neural radiance fields (NeRFs) have received significant attention due to their high-quality novel view rendering ability, prompting research to address various real-world cases. One critical challenge is the camera motion blur caused by camera movement during exposure time, which prevents accurate 3D scene reconstruction. In this study, we propose continuous rigid motion-aware gaussian splatting (CRiM-GS) to reconstruct accurate 3D scene from blurry images with real-time rendering speed. Considering the actual camera motion blurring process, which consists of complex motion patterns, we predict the continuous movement of the camera based on neural ordinary differential equations (ODEs). Specifically, we leverage rigid body transformations to model the camera motion with proper regularization, preserving the shape and size of the object. Furthermore, we introduce a continuous deformable 3D transformation in the SE(3) field to adapt the rigid body transformation to real-world problems by ensuring a higher degree of freedom. By revisiting fundamental camera theory and employing advanced neural network training techniques, we achieve accurate modeling of continuous camera trajectories. We conduct extensive experiments, demonstrating state-of-the-art performance both quantitatively and qualitatively on benchmark datasets.

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for studying hyperbolic geometry, some works have attempted to build principled generalizations of Euclidean neural networks on matrix manifolds. However, due to the lack of many concepts in gyrovector spaces for the considered manifolds, e.g., the inner product and gyroangles, techniques and mathematical tools provided by these works are still limited compared to those developed for studying hyperbolic geometry. In this paper, we generalize some notions in gyrovector spaces for SPD and Grassmann manifolds, and propose new models and layers for building neural networks on these manifolds. We show the effectiveness of our approach in two applications, i.e., human action recognition and knowledge graph completion.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

In this research, we present a novel approach to motion customization in video generation, addressing the widespread gap in the thorough exploration of motion representation within video generative models. Recognizing the unique challenges posed by video's spatiotemporal nature, our method introduces Motion Embeddings, a set of explicit, temporally coherent one-dimensional embeddings derived from a given video. These embeddings are designed to integrate seamlessly with the temporal transformer modules of video diffusion models, modulating self-attention computations across frames without compromising spatial integrity. Our approach offers a compact and efficient solution to motion representation and enables complex manipulations of motion characteristics through vector arithmetic in the embedding space. Furthermore, we identify the Temporal Discrepancy in video generative models, which refers to variations in how different motion modules process temporal relationships between frames. We leverage this understanding to optimize the integration of our motion embeddings. Our contributions include the introduction of a tailored motion embedding for customization tasks, insights into the temporal processing differences in video models, and a demonstration of the practical advantages and effectiveness of our method through extensive experiments.

State-of-the-art text-to-motion generation models rely on the kinematic-aware, local-relative motion representation popularized by HumanML3D, which encodes motion relative to the pelvis and to the previous frame with built-in redundancy. While this design simplifies training for earlier generation models, it introduces critical limitations for diffusion models and hinders applicability to downstream tasks. In this work, we revisit the motion representation and propose a radically simplified and long-abandoned alternative for text-to-motion generation: absolute joint coordinates in global space. Through systematic analysis of design choices, we show that this formulation achieves significantly higher motion fidelity, improved text alignment, and strong scalability, even with a simple Transformer backbone and no auxiliary kinematic-aware losses. Moreover, our formulation naturally supports downstream tasks such as text-driven motion control and temporal/spatial editing without additional task-specific reengineering and costly classifier guidance generation from control signals. Finally, we demonstrate promising generalization to directly generate SMPL-H mesh vertices in motion from text, laying a strong foundation for future research and motion-related applications.

We introduce MotionCrafter, a video diffusion-based framework that jointly reconstructs 4D geometry and estimates dense motion from a monocular video. The core of our method is a novel joint representation of dense 3D point maps and 3D scene flows in a shared coordinate system, and a novel 4D VAE to effectively learn this representation. Unlike prior work that forces the 3D value and latents to align strictly with RGB VAE latents-despite their fundamentally different distributions-we show that such alignment is unnecessary and leads to suboptimal performance. Instead, we introduce a new data normalization and VAE training strategy that better transfers diffusion priors and greatly improves reconstruction quality. Extensive experiments across multiple datasets demonstrate that MotionCrafter achieves state-of-the-art performance in both geometry reconstruction and dense scene flow estimation, delivering 38.64% and 25.0% improvements in geometry and motion reconstruction, respectively, all without any post-optimization. Project page: https://ruijiezhu94.github.io/MotionCrafter_Page

Objects in videos are typically characterized by continuous smooth motion. We exploit continuous smooth motion in three ways. 1) Improved accuracy by using object motion as an additional source of supervision, which we obtain by anticipating object locations from a static keyframe. 2) Improved efficiency by only doing the expensive feature computations on a small subset of all frames. Because neighboring video frames are often redundant, we only compute features for a single static keyframe and predict object locations in subsequent frames. 3) Reduced annotation cost, where we only annotate the keyframe and use smooth pseudo-motion between keyframes. We demonstrate computational efficiency, annotation efficiency, and improved mean average precision compared to the state-of-the-art on four datasets: ImageNet VID, EPIC KITCHENS-55, YouTube-BoundingBoxes, and Waymo Open dataset. Our source code is available at https://github.com/L-KID/Videoobject-detection-by-location-anticipation.

Volumetric video is emerging as a key medium for digitizing the dynamic physical world, creating the virtual environments with six degrees of freedom to deliver immersive user experiences. However, robustly modeling general dynamic scenes, especially those involving topological changes while maintaining long-term tracking remains a fundamental challenge. In this paper, we present TaoGS, a novel topology-aware dynamic Gaussian representation that disentangles motion and appearance to support, both, long-range tracking and topological adaptation. We represent scene motion with a sparse set of motion Gaussians, which are continuously updated by a spatio-temporal tracker and photometric cues that detect structural variations across frames. To capture fine-grained texture, each motion Gaussian anchors and dynamically activates a set of local appearance Gaussians, which are non-rigidly warped to the current frame to provide strong initialization and significantly reduce training time. This activation mechanism enables efficient modeling of detailed textures and maintains temporal coherence, allowing high-fidelity rendering even under challenging scenarios such as changing clothes. To enable seamless integration into codec-based volumetric formats, we introduce a global Gaussian Lookup Table that records the lifespan of each Gaussian and organizes attributes into a lifespan-aware 2D layout. This structure aligns naturally with standard video codecs and supports up to 40 compression. TaoGS provides a unified, adaptive solution for scalable volumetric video under topological variation, capturing moments where "elegance in motion" and "Power in Stillness", delivering immersive experiences that harmonize with the physical world.

Recent 4D shape representations model continuous temporal evolution of implicit shapes by (1) learning query flows without leveraging shape and articulation priors or (2) decoding shape occupancies separately for each time value. Thus, they do not effectively capture implicit correspondences between articulated shapes or regularize jittery temporal deformations. In this work, we present FourierHandFlow, which is a spatio-temporally continuous representation for human hands that combines a 3D occupancy field with articulation-aware query flows represented as Fourier series. Given an input RGB sequence, we aim to learn a fixed number of Fourier coefficients for each query flow to guarantee smooth and continuous temporal shape dynamics. To effectively model spatio-temporal deformations of articulated hands, we compose our 4D representation based on two types of Fourier query flow: (1) pose flow that models query dynamics influenced by hand articulation changes via implicit linear blend skinning and (2) shape flow that models query-wise displacement flow. In the experiments, our method achieves state-of-the-art results on video-based 4D reconstruction while being computationally more efficient than the existing 3D/4D implicit shape representations. We additionally show our results on motion inter- and extrapolation and texture transfer using the learned correspondences of implicit shapes. To the best of our knowledge, FourierHandFlow is the first neural 4D continuous hand representation learned from RGB videos. The code will be publicly accessible.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.

We present a unified perspective on tackling various human-centric video tasks by learning human motion representations from large-scale and heterogeneous data resources. Specifically, we propose a pretraining stage in which a motion encoder is trained to recover the underlying 3D motion from noisy partial 2D observations. The motion representations acquired in this way incorporate geometric, kinematic, and physical knowledge about human motion, which can be easily transferred to multiple downstream tasks. We implement the motion encoder with a Dual-stream Spatio-temporal Transformer (DSTformer) neural network. It could capture long-range spatio-temporal relationships among the skeletal joints comprehensively and adaptively, exemplified by the lowest 3D pose estimation error so far when trained from scratch. Furthermore, our proposed framework achieves state-of-the-art performance on all three downstream tasks by simply finetuning the pretrained motion encoder with a simple regression head (1-2 layers), which demonstrates the versatility of the learned motion representations.

Text-motion retrieval aims to learn a semantically aligned latent space between natural language descriptions and 3D human motion skeleton sequences, enabling bidirectional search across the two modalities. Most existing methods use a dual-encoder framework that compresses motion and text into global embeddings, discarding fine-grained local correspondences, and thus reducing accuracy. Additionally, these global-embedding methods offer limited interpretability of the retrieval results. To overcome these limitations, we propose an interpretable, joint-angle-based motion representation that maps joint-level local features into a structured pseudo-image, compatible with pre-trained Vision Transformers. For text-to-motion retrieval, we employ MaxSim, a token-wise late interaction mechanism, and enhance it with Masked Language Modeling regularization to foster robust, interpretable text-motion alignment. Extensive experiments on HumanML3D and KIT-ML show that our method outperforms state-of-the-art text-motion retrieval approaches while offering interpretable fine-grained correspondences between text and motion. The code is available in the supplementary material.

We present DIMO, a generative approach capable of generating diverse 3D motions for arbitrary objects from a single image. The core idea of our work is to leverage the rich priors in well-trained video models to extract the common motion patterns and then embed them into a shared low-dimensional latent space. Specifically, we first generate multiple videos of the same object with diverse motions. We then embed each motion into a latent vector and train a shared motion decoder to learn the distribution of motions represented by a structured and compact motion representation, i.e., neural key point trajectories. The canonical 3D Gaussians are then driven by these key points and fused to model the geometry and appearance. During inference time with learned latent space, we can instantly sample diverse 3D motions in a single-forward pass and support several interesting applications including 3D motion interpolation and language-guided motion generation. Our project page is available at https://linzhanm.github.io/dimo.

3D reconstruction in dynamic scenes primarily relies on the combination of geometry estimation and matching modules where the latter task is pivotal for distinguishing dynamic regions which can help to mitigate the interference introduced by camera and object motion. Furthermore, the matching module explicitly models object motion, enabling the tracking of specific targets and advancing motion understanding in complex scenarios. Recently, the proposed representation of pointmap in DUSt3R suggests a potential solution to unify both geometry estimation and matching in 3D space, but it still struggles with ambiguous matching in dynamic regions, which may hamper further improvement. In this work, we present POMATO, a unified framework for dynamic 3D reconstruction by marrying pointmap matching with temporal motion. Specifically, our method first learns an explicit matching relationship by mapping RGB pixels from both dynamic and static regions across different views to 3D pointmaps within a unified coordinate system. Furthermore, we introduce a temporal motion module for dynamic motions that ensures scale consistency across different frames and enhances performance in tasks requiring both precise geometry and reliable matching, most notably 3D point tracking. We show the effectiveness of the proposed pointmap matching and temporal fusion paradigm by demonstrating the remarkable performance across multiple downstream tasks, including video depth estimation, 3D point tracking, and pose estimation. Code and models are publicly available at https://github.com/wyddmw/POMATO.

We consider the problem of efficiently representing casually captured monocular videos in a spatially- and temporally-coherent manner. While existing approaches predominantly rely on 2D/2.5D techniques treating videos as collections of spatiotemporal pixels, they struggle with complex motions, occlusions, and geometric consistency due to absence of temporal coherence and explicit 3D structure. Drawing inspiration from monocular video as a projection of the dynamic 3D world, we explore representing videos in their intrinsic 3D form through continuous flows of Gaussian primitives in space-time. In this paper, we propose NutWorld, a novel framework that efficiently transforms monocular videos into dynamic 3D Gaussian representations in a single forward pass. At its core, NutWorld introduces a structured spatial-temporal aligned Gaussian (STAG) representation, enabling optimization-free scene modeling with effective depth and flow regularization. Through comprehensive experiments, we demonstrate that NutWorld achieves high-fidelity video reconstruction quality while enabling various downstream applications in real-time. Demos and code will be available at https://github.com/Nut-World/NutWorld.

Image animation consists of generating a video sequence so that an object in a source image is animated according to the motion of a driving video. Our framework addresses this problem without using any annotation or prior information about the specific object to animate. Once trained on a set of videos depicting objects of the same category (e.g. faces, human bodies), our method can be applied to any object of this class. To achieve this, we decouple appearance and motion information using a self-supervised formulation. To support complex motions, we use a representation consisting of a set of learned keypoints along with their local affine transformations. A generator network models occlusions arising during target motions and combines the appearance extracted from the source image and the motion derived from the driving video. Our framework scores best on diverse benchmarks and on a variety of object categories. Our source code is publicly available.

The objective of this paper is motion segmentation -- discovering and segmenting the moving objects in a video. This is a much studied area with numerous careful,and sometimes complex, approaches and training schemes including: self-supervised learning, learning from synthetic datasets, object-centric representations, amodal representations, and many more. Our interest in this paper is to determine if the Segment Anything model (SAM) can contribute to this task. We investigate two models for combining SAM with optical flow that harness the segmentation power of SAM with the ability of flow to discover and group moving objects. In the first model, we adapt SAM to take optical flow, rather than RGB, as an input. In the second, SAM takes RGB as an input, and flow is used as a segmentation prompt. These surprisingly simple methods, without any further modifications, outperform all previous approaches by a considerable margin in both single and multi-object benchmarks. We also extend these frame-level segmentations to sequence-level segmentations that maintain object identity. Again, this simple model outperforms previous methods on multiple video object segmentation benchmarks.

Customized video generation aims to produce videos that faithfully preserve the subject's appearance from reference images while maintaining temporally consistent motion from reference videos. Existing methods struggle to ensure both subject appearance similarity and motion pattern consistency due to the lack of object-level guidance for subject and motion. To address this, we propose SMRABooth, which leverages the self-supervised encoder and optical flow encoder to provide object-level subject and motion representations. These representations are aligned with the model during the LoRA fine-tuning process. Our approach is structured in three core stages: (1) We exploit subject representations via a self-supervised encoder to guide subject alignment, enabling the model to capture overall structure of subject and enhance high-level semantic consistency. (2) We utilize motion representations from an optical flow encoder to capture structurally coherent and object-level motion trajectories independent of appearance. (3) We propose a subject-motion association decoupling strategy that applies sparse LoRAs injection across both locations and timing, effectively reducing interference between subject and motion LoRAs. Extensive experiments show that SMRABooth excels in subject and motion customization, maintaining consistent subject appearance and motion patterns, proving its effectiveness in controllable text-to-video generation.

We present Manifold Diffusion Fields (MDF), an approach to learn generative models of continuous functions defined over Riemannian manifolds. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on the manifold via the eigen-functions of the Laplace-Beltrami Operator. MDF represents functions using an explicit parametrization formed by a set of multiple input-output pairs. Our approach allows to sample continuous functions on manifolds and is invariant with respect to rigid and isometric transformations of the manifold. Empirical results on several datasets and manifolds show that MDF can capture distributions of such functions with better diversity and fidelity than previous approaches.

Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been adapted to several manifolds, referred to as Riemannian normalization. Nonetheless, most of the existing Riemannian normalization methods have been derived in an ad hoc manner and only apply to specific manifolds. This paper establishes a unified framework for Riemannian Batch Normalization (RBN) techniques on Lie groups. Our framework offers the theoretical guarantee of controlling both the Riemannian mean and variance. Empirically, we focus on Symmetric Positive Definite (SPD) manifolds, which possess three distinct types of Lie group structures. Using the deformation concept, we generalize the existing Lie groups on SPD manifolds into three families of parameterized Lie groups. Specific normalization layers induced by these Lie groups are then proposed for SPD neural networks. We demonstrate the effectiveness of our approach through three sets of experiments: radar recognition, human action recognition, and electroencephalography (EEG) classification. The code is available at https://github.com/GitZH-Chen/LieBN.git.

We present 4RC, a unified feed-forward framework for 4D reconstruction from monocular videos. Unlike existing approaches that typically decouple motion from geometry or produce limited 4D attributes such as sparse trajectories or two-view scene flow, 4RC learns a holistic 4D representation that jointly captures dense scene geometry and motion dynamics. At its core, 4RC introduces a novel encode-once, query-anywhere and anytime paradigm: a transformer backbone encodes the entire video into a compact spatio-temporal latent space, from which a conditional decoder can efficiently query 3D geometry and motion for any query frame at any target timestamp. To facilitate learning, we represent per-view 4D attributes in a minimally factorized form by decomposing them into base geometry and time-dependent relative motion. Extensive experiments demonstrate that 4RC outperforms prior and concurrent methods across a wide range of 4D reconstruction tasks.

This paper addresses the task of space-time video super-resolution (ST-VSR). Existing methods generally suffer from inaccurate motion estimation and motion compensation (MEMC) problems for large motions. Inspired by recent progress in physics-informed neural networks, we model the challenges of MEMC in ST-VSR as a mapping between two continuous function spaces. Specifically, our approach transforms independent low-resolution representations in the coarse-grained continuous function space into refined representations with enriched spatiotemporal details in the fine-grained continuous function space. To achieve efficient and accurate MEMC, we design a Galerkin-type attention function to perform frame alignment and temporal interpolation. Due to the linear complexity of the Galerkin-type attention mechanism, our model avoids patch partitioning and offers global receptive fields, enabling precise estimation of large motions. The experimental results show that the proposed method surpasses state-of-the-art techniques in both fixed-size and continuous space-time video super-resolution tasks.

Reality is a dance between rigid constraints and deformable structures. For video models, that means generating motion that preserves fidelity as well as structure. Despite progress in diffusion models, producing realistic structure-preserving motion remains challenging, especially for articulated and deformable objects such as humans and animals. Scaling training data alone, so far, has failed to resolve physically implausible transitions. Existing approaches rely on conditioning with noisy motion representations, such as optical flow or skeletons extracted using an external imperfect model. To address these challenges, we introduce an algorithm to distill structure-preserving motion priors from an autoregressive video tracking model (SAM2) into a bidirectional video diffusion model (CogVideoX). With our method, we train SAM2VideoX, which contains two innovations: (1) a bidirectional feature fusion module that extracts global structure-preserving motion priors from a recurrent model like SAM2; (2) a Local Gram Flow loss that aligns how local features move together. Experiments on VBench and in human studies show that SAM2VideoX delivers consistent gains (+2.60\% on VBench, 21-22\% lower FVD, and 71.4\% human preference) over prior baselines. Specifically, on VBench, we achieve 95.51\%, surpassing REPA (92.91\%) by 2.60\%, and reduce FVD to 360.57, a 21.20\% and 22.46\% improvement over REPA- and LoRA-finetuning, respectively. The project website can be found at https://sam2videox.github.io/ .

Effective spatio-temporal representation is fundamental to modeling, understanding, and predicting dynamics in videos. The atomic unit of a video, the pixel, traces a continuous 3D trajectory over time, serving as the primitive element of dynamics. Based on this principle, we propose representing any video as a Trajectory Field: a dense mapping that assigns a continuous 3D trajectory function of time to each pixel in every frame. With this representation, we introduce Trace Anything, a neural network that predicts the entire trajectory field in a single feed-forward pass. Specifically, for each pixel in each frame, our model predicts a set of control points that parameterizes a trajectory (i.e., a B-spline), yielding its 3D position at arbitrary query time instants. We trained the Trace Anything model on large-scale 4D data, including data from our new platform, and our experiments demonstrate that: (i) Trace Anything achieves state-of-the-art performance on our new benchmark for trajectory field estimation and performs competitively on established point-tracking benchmarks; (ii) it offers significant efficiency gains thanks to its one-pass paradigm, without requiring iterative optimization or auxiliary estimators; and (iii) it exhibits emergent abilities, including goal-conditioned manipulation, motion forecasting, and spatio-temporal fusion. Project page: https://trace-anything.github.io/.

Dynamic human rendering from video sequences has achieved remarkable progress by formulating the rendering as a mapping from static poses to human images. However, existing methods focus on the human appearance reconstruction of every single frame while the temporal motion relations are not fully explored. In this paper, we propose a new 4D motion modeling paradigm, SurMo, that jointly models the temporal dynamics and human appearances in a unified framework with three key designs: 1) Surface-based motion encoding that models 4D human motions with an efficient compact surface-based triplane. It encodes both spatial and temporal motion relations on the dense surface manifold of a statistical body template, which inherits body topology priors for generalizable novel view synthesis with sparse training observations. 2) Physical motion decoding that is designed to encourage physical motion learning by decoding the motion triplane features at timestep t to predict both spatial derivatives and temporal derivatives at the next timestep t+1 in the training stage. 3) 4D appearance decoding that renders the motion triplanes into images by an efficient volumetric surface-conditioned renderer that focuses on the rendering of body surfaces with motion learning conditioning. Extensive experiments validate the state-of-the-art performance of our new paradigm and illustrate the expressiveness of surface-based motion triplanes for rendering high-fidelity view-consistent humans with fast motions and even motion-dependent shadows. Our project page is at: https://taohuumd.github.io/projects/SurMo/

Text-to-motion generation is a formidable task, aiming to produce human motions that align with the input text while also adhering to human capabilities and physical laws. While there have been advancements in diffusion models, their application in discrete spaces remains underexplored. Current methods often overlook the varying significance of different motions, treating them uniformly. It is essential to recognize that not all motions hold the same relevance to a particular textual description. Some motions, being more salient and informative, should be given precedence during generation. In response, we introduce a Priority-Centric Motion Discrete Diffusion Model (M2DM), which utilizes a Transformer-based VQ-VAE to derive a concise, discrete motion representation, incorporating a global self-attention mechanism and a regularization term to counteract code collapse. We also present a motion discrete diffusion model that employs an innovative noise schedule, determined by the significance of each motion token within the entire motion sequence. This approach retains the most salient motions during the reverse diffusion process, leading to more semantically rich and varied motions. Additionally, we formulate two strategies to gauge the importance of motion tokens, drawing from both textual and visual indicators. Comprehensive experiments on the HumanML3D and KIT-ML datasets confirm that our model surpasses existing techniques in fidelity and diversity, particularly for intricate textual descriptions.

In this paper, we are interested in self-supervised learning the motion cues in videos using dynamic motion filters for a better motion representation to finally boost human action recognition in particular. Thus far, the vision community has focused on spatio-temporal approaches using standard filters, rather we here propose dynamic filters that adaptively learn the video-specific internal motion representation by predicting the short-term future frames. We name this new motion representation, as dynamic motion representation (DMR) and is embedded inside of 3D convolutional network as a new layer, which captures the visual appearance and motion dynamics throughout entire video clip via end-to-end network learning. Simultaneously, we utilize these motion representation to enrich video classification. We have designed the frame prediction task as an auxiliary task to empower the classification problem. With these overall objectives, to this end, we introduce a novel unified spatio-temporal 3D-CNN architecture (DynamoNet) that jointly optimizes the video classification and learning motion representation by predicting future frames as a multi-task learning problem. We conduct experiments on challenging human action datasets: Kinetics 400, UCF101, HMDB51. The experiments using the proposed DynamoNet show promising results on all the datasets.

This paper presents a new, provably-convergent algorithm for computing the flag-mean and flag-median of a set of points on a flag manifold under the chordal metric. The flag manifold is a mathematical space consisting of flags, which are sequences of nested subspaces of a vector space that increase in dimension. The flag manifold is a superset of a wide range of known matrix spaces, including Stiefel and Grassmanians, making it a general object that is useful in a wide variety computer vision problems. To tackle the challenge of computing first order flag statistics, we first transform the problem into one that involves auxiliary variables constrained to the Stiefel manifold. The Stiefel manifold is a space of orthogonal frames, and leveraging the numerical stability and efficiency of Stiefel-manifold optimization enables us to compute the flag-mean effectively. Through a series of experiments, we show the competence of our method in Grassmann and rotation averaging, as well as principal component analysis. We release our source code under https://github.com/nmank/FlagAveraging.

Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion. We introduce TORA, a topology-first representation alignment framework that distills relational structure from a frozen pretrained 3D encoder into the flow-matching backbone during training. We first realize this via simple instantiation, token-wise cosine matching, which injects the learned geometric descriptors from the teacher representation. We then extend to employ a Centered Kernel Alignment (CKA) loss to match the similarity structure between student and teacher representations for enhanced topological alignment. Through systematic probing of diverse 3D encoders, we show that geometry- and contact-centric teacher properties, not semantic classification ability, govern alignment effectiveness, and that alignment is most beneficial at later transformer layers where spatial structure naturally emerges. TORA introduces zero inference overhead while yielding two consistent benefits: faster convergence (up to 6.9times) and improved accuracy in-distribution, along with greater robustness under domain shift. Experiments on five benchmarks spanning geometric, semantic, and inter-object assembly demonstrate state-of-the-art performance, with particularly pronounced gains in zero-shot transfer to unseen real-world and synthetic datasets. Project page: https://nahyuklee.github.io/tora.

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations obtained by local PCAs are collected into a rank k tangent subbundle on R^d, k<d, which we call a principal subbundle. This determines a sub-Riemannian metric on R^d. We show that sub-Riemannian geodesics with respect to this metric can successfully be applied to a number of important problems, such as: explicit construction of an approximating submanifold M, construction of a representation of the point-cloud in R^k, and computation of distances between observations, taking the learned geometry into account. The reconstruction is guaranteed to equal the true submanifold in the limit case where tangent spaces are estimated exactly. Via simulations, we show that the framework is robust when applied to noisy data. Furthermore, the framework generalizes to observations on an a priori known Riemannian manifold.

Existing methods for the 4D reconstruction of general, non-rigidly deforming objects focus on novel-view synthesis and neglect correspondences. However, time consistency enables advanced downstream tasks like 3D editing, motion analysis, or virtual-asset creation. We propose SceNeRFlow to reconstruct a general, non-rigid scene in a time-consistent manner. Our dynamic-NeRF method takes multi-view RGB videos and background images from static cameras with known camera parameters as input. It then reconstructs the deformations of an estimated canonical model of the geometry and appearance in an online fashion. Since this canonical model is time-invariant, we obtain correspondences even for long-term, long-range motions. We employ neural scene representations to parametrize the components of our method. Like prior dynamic-NeRF methods, we use a backwards deformation model. We find non-trivial adaptations of this model necessary to handle larger motions: We decompose the deformations into a strongly regularized coarse component and a weakly regularized fine component, where the coarse component also extends the deformation field into the space surrounding the object, which enables tracking over time. We show experimentally that, unlike prior work that only handles small motion, our method enables the reconstruction of studio-scale motions.

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are neural networks by introducing a distance between the hidden layer representations of the neural networks. These distances are then fed to the non-linear dimensionality reduction algorithm PHATE to create a manifold of neural networks. We characterize this manifold using features of the representation, including class separation, hierarchical cluster structure, spectral entropy, and topological structure. Our analysis reveals that high-performing networks cluster together in the manifold, displaying consistent embedding patterns across all these features. Finally, we demonstrate the utility of this approach for guiding hyperparameter optimization and neural architecture search by sampling from the manifold.

Image analysis in the euclidean space through linear hyperspaces is well studied. However, in the quest for more effective image representations, we turn to hyperbolic manifolds. They provide a compelling alternative to capture complex hierarchical relationships in images with remarkably small dimensionality. To demonstrate hyperbolic embeddings' competence, we introduce a light-weight hyperbolic graph neural network for image segmentation, encompassing patch-level features in a very small embedding size. Our solution, Seg-HGNN, surpasses the current best unsupervised method by 2.5\%, 4\% on VOC-07, VOC-12 for localization, and by 0.8\%, 1.3\% on CUB-200, ECSSD for segmentation, respectively. With less than 7.5k trainable parameters, Seg-HGNN delivers effective and fast (approx 2 images/second) results on very standard GPUs like the GTX1650. This empirical evaluation presents compelling evidence of the efficacy and potential of hyperbolic representations for vision tasks.

Generating interactive and dynamic 4D scenes from a single static image remains a core challenge. Most existing generate-then-reconstruct and reconstruct-then-generate methods decouple geometry from motion, causing spatiotemporal inconsistencies and poor generalization. To address these, we extend the reconstruct-then-generate framework to jointly perform Motion generation and geometric Reconstruction for 4D Synthesis (MoRe4D). We first introduce TrajScene-60K, a large-scale dataset of 60,000 video samples with dense point trajectories, addressing the scarcity of high-quality 4D scene data. Based on this, we propose a diffusion-based 4D Scene Trajectory Generator (4D-STraG) to jointly generate geometrically consistent and motion-plausible 4D point trajectories. To leverage single-view priors, we design a depth-guided motion normalization strategy and a motion-aware module for effective geometry and dynamics integration. We then propose a 4D View Synthesis Module (4D-ViSM) to render videos with arbitrary camera trajectories from 4D point track representations. Experiments show that MoRe4D generates high-quality 4D scenes with multi-view consistency and rich dynamic details from a single image. Code: https://github.com/Zhangyr2022/MoRe4D.

In this paper, we show that useful video representations can be learned from synthetic videos and natural images, without incorporating natural videos in the training. We propose a progression of video datasets synthesized by simple generative processes, that model a growing set of natural video properties (e.g. motion, acceleration, and shape transformations). The downstream performance of video models pre-trained on these generated datasets gradually increases with the dataset progression. A VideoMAE model pre-trained on our synthetic videos closes 97.2% of the performance gap on UCF101 action classification between training from scratch and self-supervised pre-training from natural videos, and outperforms the pre-trained model on HMDB51. Introducing crops of static images to the pre-training stage results in similar performance to UCF101 pre-training and outperforms the UCF101 pre-trained model on 11 out of 14 out-of-distribution datasets of UCF101-P. Analyzing the low-level properties of the datasets, we identify correlations between frame diversity, frame similarity to natural data, and downstream performance. Our approach provides a more controllable and transparent alternative to video data curation processes for pre-training.

We present an approach to modeling an image-space prior on scene dynamics. Our prior is learned from a collection of motion trajectories extracted from real video sequences containing natural, oscillating motion such as trees, flowers, candles, and clothes blowing in the wind. Given a single image, our trained model uses a frequency-coordinated diffusion sampling process to predict a per-pixel long-term motion representation in the Fourier domain, which we call a neural stochastic motion texture. This representation can be converted into dense motion trajectories that span an entire video. Along with an image-based rendering module, these trajectories can be used for a number of downstream applications, such as turning still images into seamlessly looping dynamic videos, or allowing users to realistically interact with objects in real pictures.

Motion-controllable image animation is a fundamental task with a wide range of potential applications. Recent works have made progress in controlling camera or object motion via various motion representations, while they still struggle to support collaborative camera and object motion control with adaptive control granularity. To this end, we introduce 3D-aware motion representation and propose an image animation framework, called Perception-as-Control, to achieve fine-grained collaborative motion control. Specifically, we construct 3D-aware motion representation from a reference image, manipulate it based on interpreted user intentions, and perceive it from different viewpoints. In this way, camera and object motions are transformed into intuitive, consistent visual changes. Then, the proposed framework leverages the perception results as motion control signals, enabling it to support various motion-related video synthesis tasks in a unified and flexible way. Experiments demonstrate the superiority of the proposed framework. For more details and qualitative results, please refer to our project webpage: https://chen-yingjie.github.io/projects/Perception-as-Control.

Understanding and predicting motion is a fundamental component of visual intelligence. Although modern video models exhibit strong comprehension of scene dynamics, exploring multiple possible futures through full video synthesis remains prohibitively inefficient. We model scene dynamics orders of magnitude more efficiently by directly operating on a long-term motion embedding that is learned from large-scale trajectories obtained from tracker models. This enables efficient generation of long, realistic motions that fulfill goals specified via text prompts or spatial pokes. To achieve this, we first learn a highly compressed motion embedding with a temporal compression factor of 64x. In this space, we train a conditional flow-matching model to generate motion latents conditioned on task descriptions. The resulting motion distributions outperform those of both state-of-the-art video models and specialized task-specific approaches.

For computer vision systems to operate in dynamic situations, they need to be able to represent and reason about object permanence. We introduce a framework for learning to estimate 4D visual representations from monocular RGB-D, which is able to persist objects, even once they become obstructed by occlusions. Unlike traditional video representations, we encode point clouds into a continuous representation, which permits the model to attend across the spatiotemporal context to resolve occlusions. On two large video datasets that we release along with this paper, our experiments show that the representation is able to successfully reveal occlusions for several tasks, without any architectural changes. Visualizations show that the attention mechanism automatically learns to follow occluded objects. Since our approach can be trained end-to-end and is easily adaptable, we believe it will be useful for handling occlusions in many video understanding tasks. Data, code, and models are available at https://occlusions.cs.columbia.edu/.

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not perceptibly shrink or extend when manipulated, constituting a powerful and well-known prior. Mathematically, this translates to the preservation of the Riemannian metric. Neural networks offer the perfect playground to solve the surface reconstruction problem as they can approximate surfaces with arbitrary precision and allow the computation of differential geometry quantities. This paper presents an approach to inferring continuous deformable surfaces from a sequence of images, which is benchmarked against several techniques and obtains state-of-the-art performance without the need for offline training.

We consider the task of Image-to-Video (I2V) generation, which involves transforming static images into realistic video sequences based on a textual description. While recent advancements produce photorealistic outputs, they frequently struggle to create videos with accurate and consistent object motion, especially in multi-object scenarios. To address these limitations, we propose a two-stage compositional framework that decomposes I2V generation into: (i) An explicit intermediate representation generation stage, followed by (ii) A video generation stage that is conditioned on this representation. Our key innovation is the introduction of a mask-based motion trajectory as an intermediate representation, that captures both semantic object information and motion, enabling an expressive but compact representation of motion and semantics. To incorporate the learned representation in the second stage, we utilize object-level attention objectives. Specifically, we consider a spatial, per-object, masked-cross attention objective, integrating object-specific prompts into corresponding latent space regions and a masked spatio-temporal self-attention objective, ensuring frame-to-frame consistency for each object. We evaluate our method on challenging benchmarks with multi-object and high-motion scenarios and empirically demonstrate that the proposed method achieves state-of-the-art results in temporal coherence, motion realism, and text-prompt faithfulness. Additionally, we introduce \benchmark, a new challenging benchmark for single-object and multi-object I2V generation, and demonstrate our method's superiority on this benchmark. Project page is available at https://guyyariv.github.io/TTM/.

We propose a self-supervised method for learning motion-focused video representations. Existing approaches minimize distances between temporally augmented videos, which maintain high spatial similarity. We instead propose to learn similarities between videos with identical local motion dynamics but an otherwise different appearance. We do so by adding synthetic motion trajectories to videos which we refer to as tubelets. By simulating different tubelet motions and applying transformations, such as scaling and rotation, we introduce motion patterns beyond what is present in the pretraining data. This allows us to learn a video representation that is remarkably data-efficient: our approach maintains performance when using only 25% of the pretraining videos. Experiments on 10 diverse downstream settings demonstrate our competitive performance and generalizability to new domains and fine-grained actions.

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise. Injective Flows fix this by jointly learning a manifold and the distribution on it. So far, they have been limited by restrictive architectures and/or high computational cost. We lift both constraints by a new efficient estimator for the maximum likelihood loss, compatible with free-form bottleneck architectures. We further show that naively learning both the data manifold and the distribution on it can lead to divergent solutions, and use this insight to motivate a stable maximum likelihood training objective. We perform extensive experiments on toy, tabular and image data, demonstrating the competitive performance of the resulting model.

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and other architectures. Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning reduced dimensional representations of the nonlinear Burgers Equations, Constrained Mechanical Systems, and spatial fields of Reaction-Diffusion Systems. GD-VAEs provide methods that can be used to obtain representations in manifold latent spaces for diverse learning tasks involving dynamics.

The manifold hypothesis posits that high-dimensional data often lies on a lower-dimensional manifold and that utilizing this manifold as the target space yields more efficient representations. While numerous traditional manifold-based techniques exist for dimensionality reduction, their application in self-supervised learning has witnessed slow progress. The recent MSimCLR method combines manifold encoding with SimCLR but requires extremely low target encoding dimensions to outperform SimCLR, limiting its applicability. This paper introduces a novel learning paradigm using an unbalanced atlas (UA), capable of surpassing state-of-the-art self-supervised learning approaches. We investigated and engineered the DeepInfomax with an unbalanced atlas (DIM-UA) method by adapting the Spatiotemporal DeepInfomax (ST-DIM) framework to align with our proposed UA paradigm. The efficacy of DIM-UA is demonstrated through training and evaluation on the Atari Annotated RAM Interface (AtariARI) benchmark, a modified version of the Atari 2600 framework that produces annotated image samples for representation learning. The UA paradigm improves existing algorithms significantly as the number of target encoding dimensions grows. For instance, the mean F1 score averaged over categories of DIM-UA is ~75% compared to ~70% of ST-DIM when using 16384 hidden units.

Due to recent advances in pose-estimation methods, human motion can be extracted from a common video in the form of 3D skeleton sequences. Despite wonderful application opportunities, effective and efficient content-based access to large volumes of such spatio-temporal skeleton data still remains a challenging problem. In this paper, we propose a novel content-based text-to-motion retrieval task, which aims at retrieving relevant motions based on a specified natural-language textual description. To define baselines for this uncharted task, we employ the BERT and CLIP language representations to encode the text modality and successful spatio-temporal models to encode the motion modality. We additionally introduce our transformer-based approach, called Motion Transformer (MoT), which employs divided space-time attention to effectively aggregate the different skeleton joints in space and time. Inspired by the recent progress in text-to-image/video matching, we experiment with two widely-adopted metric-learning loss functions. Finally, we set up a common evaluation protocol by defining qualitative metrics for assessing the quality of the retrieved motions, targeting the two recently-introduced KIT Motion-Language and HumanML3D datasets. The code for reproducing our results is available at https://github.com/mesnico/text-to-motion-retrieval.

Recovering dense and long-range pixel motion in videos is a challenging problem. Part of the difficulty arises from the 3D-to-2D projection process, leading to occlusions and discontinuities in the 2D motion domain. While 2D motion can be intricate, we posit that the underlying 3D motion can often be simple and low-dimensional. In this work, we propose to estimate point trajectories in 3D space to mitigate the issues caused by image projection. Our method, named SpatialTracker, lifts 2D pixels to 3D using monocular depth estimators, represents the 3D content of each frame efficiently using a triplane representation, and performs iterative updates using a transformer to estimate 3D trajectories. Tracking in 3D allows us to leverage as-rigid-as-possible (ARAP) constraints while simultaneously learning a rigidity embedding that clusters pixels into different rigid parts. Extensive evaluation shows that our approach achieves state-of-the-art tracking performance both qualitatively and quantitatively, particularly in challenging scenarios such as out-of-plane rotation.

Motion modeling is critical in flow-based Video Frame Interpolation (VFI). Existing paradigms either consider linear combinations of bidirectional flows or directly predict bilateral flows for given timestamps without exploring favorable motion priors, thus lacking the capability of effectively modeling spatiotemporal dynamics in real-world videos. To address this limitation, in this study, we introduce Generalizable Implicit Motion Modeling (GIMM), a novel and effective approach to motion modeling for VFI. Specifically, to enable GIMM as an effective motion modeling paradigm, we design a motion encoding pipeline to model spatiotemporal motion latent from bidirectional flows extracted from pre-trained flow estimators, effectively representing input-specific motion priors. Then, we implicitly predict arbitrary-timestep optical flows within two adjacent input frames via an adaptive coordinate-based neural network, with spatiotemporal coordinates and motion latent as inputs. Our GIMM can be smoothly integrated with existing flow-based VFI works without further modifications. We show that GIMM performs better than the current state of the art on the VFI benchmarks.

In this paper, we present a method for unconstrained end-to-end head pose estimation. We address the problem of ambiguous rotation labels by introducing the rotation matrix formalism for our ground truth data and propose a continuous 6D rotation matrix representation for efficient and robust direct regression. This way, our method can learn the full rotation appearance which is contrary to previous approaches that restrict the pose prediction to a narrow-angle for satisfactory results. In addition, we propose a geodesic distance-based loss to penalize our network with respect to the SO(3) manifold geometry. Experiments on the public AFLW2000 and BIWI datasets demonstrate that our proposed method significantly outperforms other state-of-the-art methods by up to 20\%. We open-source our training and testing code along with our pre-trained models: https://github.com/thohemp/6DRepNet.

Controlling human motion based on text presents an important challenge in computer vision. Traditional approaches often rely on holistic action descriptions for motion synthesis, which struggle to capture subtle movements of local body parts. This limitation restricts the ability to isolate and manipulate specific movements. To address this, we propose a novel motion representation that decomposes motion into distinct body joint group movements and interactions from a kinematic perspective. We design an automatic dataset collection pipeline that enhances the existing text-motion benchmark by incorporating fine-grained local joint-group motion and interaction descriptions. To bridge the gap between text and motion domains, we introduce a hierarchical motion semantics approach that progressively fuses joint-level interaction information into the global action-level semantics for modality alignment. With this hierarchy, we introduce a coarse-to-fine motion synthesis procedure for various generation and editing downstream applications. Our quantitative and qualitative experiments demonstrate that the proposed formulation enhances text-motion retrieval by improving joint-spatial understanding, and enables more precise joint-motion generation and control. Project Page: {\smallhttps://andypinxinliu.github.io/KinMo/}

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space. Stacking the encoder and decoder together constructs an autoencoder, which we term a diffusion net, that performs out-of-sample-extension as well as outlier detection. We introduce new neural net constraints for the encoder, which preserves the local geometry of the points, and we prove rates of convergence for the encoder. Also, our approach is efficient in both computational complexity and memory requirements, as opposed to previous methods that require storage of all training points in both the high-dimensional and the low-dimensional spaces to calculate the out-of-sample-extension and the pre-image.

We present Lang2Motion, a framework for language-guided point trajectory generation by aligning motion manifolds with joint embedding spaces. Unlike prior work focusing on human motion or video synthesis, we generate explicit trajectories for arbitrary objects using motion extracted from real-world videos via point tracking. Our transformer-based auto-encoder learns trajectory representations through dual supervision: textual motion descriptions and rendered trajectory visualizations, both mapped through CLIP's frozen encoders. Lang2Motion achieves 34.2% Recall@1 on text-to-trajectory retrieval, outperforming video-based methods by 12.5 points, and improves motion accuracy by 33-52% (12.4 ADE vs 18.3-25.3) compared to video generation baselines. We demonstrate 88.3% Top-1 accuracy on human action recognition despite training only on diverse object motions, showing effective transfer across motion domains. Lang2Motion supports style transfer, semantic interpolation, and latent-space editing through CLIP-aligned trajectory representations.

This paper addresses the challenge of learning semantically and functionally meaningful 3D motion priors from real-world videos, in order to enable prediction of future 3D scene motion from a single input image. We propose a novel pixel-aligned Motion Map (MoMap) representation for 3D scene motion, which can be generated from existing generative image models to facilitate efficient and effective motion prediction. To learn meaningful distributions over motion, we create a large-scale database of MoMaps from over 50,000 real videos and train a diffusion model on these representations. Our motion generation not only synthesizes trajectories in 3D but also suggests a new pipeline for 2D video synthesis: first generate a MoMap, then warp an image accordingly and complete the warped point-based renderings. Experimental results demonstrate that our approach generates plausible and semantically consistent 3D scene motion.

Gaussian splatting has emerged as a powerful tool for high-fidelity reconstruction of dynamic scenes. However, existing methods primarily rely on implicit motion representations, such as encoding motions into neural networks or per-Gaussian parameters, which makes it difficult to further manipulate the reconstructed motions. This lack of explicit controllability limits existing methods to replaying recorded motions only, which hinders a wider application in robotics. To address this, we propose Motion Blender Gaussian Splatting (MBGS), a novel framework that uses motion graphs as an explicit and sparse motion representation. The motion of a graph's links is propagated to individual Gaussians via dual quaternion skinning, with learnable weight painting functions that determine the influence of each link. The motion graphs and 3D Gaussians are jointly optimized from input videos via differentiable rendering. Experiments show that MBGS achieves state-of-the-art performance on the highly challenging iPhone dataset while being competitive on HyperNeRF. We demonstrate the application potential of our method in animating novel object poses, synthesizing real robot demonstrations, and predicting robot actions through visual planning. The source code, models, video demonstrations can be found at http://mlzxy.github.io/motion-blender-gs.

Learning a good representation for space-time correspondence is the key for various computer vision tasks, including tracking object bounding boxes and performing video object pixel segmentation. To learn generalizable representation for correspondence in large-scale, a variety of self-supervised pretext tasks are proposed to explicitly perform object-level or patch-level similarity learning. Instead of following the previous literature, we propose to learn correspondence using Video Frame-level Similarity (VFS) learning, i.e, simply learning from comparing video frames. Our work is inspired by the recent success in image-level contrastive learning and similarity learning for visual recognition. Our hypothesis is that if the representation is good for recognition, it requires the convolutional features to find correspondence between similar objects or parts. Our experiments show surprising results that VFS surpasses state-of-the-art self-supervised approaches for both OTB visual object tracking and DAVIS video object segmentation. We perform detailed analysis on what matters in VFS and reveals new properties on image and frame level similarity learning. Project page with code is available at https://jerryxu.net/VFS

Video world models aim to simulate dynamic, real-world environments, yet existing methods struggle to provide unified and precise control over camera and multi-object motion, as videos inherently operate dynamics in the projected 2D image plane. To bridge this gap, we introduce VerseCrafter, a 4D-aware video world model that enables explicit and coherent control over both camera and object dynamics within a unified 4D geometric world state. Our approach is centered on a novel 4D Geometric Control representation, which encodes the world state through a static background point cloud and per-object 3D Gaussian trajectories. This representation captures not only an object's path but also its probabilistic 3D occupancy over time, offering a flexible, category-agnostic alternative to rigid bounding boxes or parametric models. These 4D controls are rendered into conditioning signals for a pretrained video diffusion model, enabling the generation of high-fidelity, view-consistent videos that precisely adhere to the specified dynamics. Unfortunately, another major challenge lies in the scarcity of large-scale training data with explicit 4D annotations. We address this by developing an automatic data engine that extracts the required 4D controls from in-the-wild videos, allowing us to train our model on a massive and diverse dataset.

Despite significant advancements in human motion generation, current motion representations, typically formulated as discrete frame sequences, still face two critical limitations: (i) they fail to capture motion from a multi-scale perspective, limiting the capability in complex patterns modeling; (ii) they lack compositional flexibility, which is crucial for model's generalization in diverse generation tasks. To address these challenges, we introduce MSQ, a novel quantization method that compresses the motion sequence into multi-scale discrete tokens across spatial and temporal dimensions. MSQ employs distinct encoders to capture body parts at varying spatial granularities and temporally interpolates the encoded features into multiple scales before quantizing them into discrete tokens. Building on this representation, we establish a generative mask modeling model to effectively support motion editing, motion control, and conditional motion generation. Through quantitative and qualitative analysis, we show that our quantization method enables the seamless composition of motion tokens without requiring specialized design or re-training. Furthermore, extensive evaluations demonstrate that our approach outperforms existing baseline methods on various benchmarks.

Estimating geometry from dynamic scenes, where objects move and deform over time, remains a core challenge in computer vision. Current approaches often rely on multi-stage pipelines or global optimizations that decompose the problem into subtasks, like depth and flow, leading to complex systems prone to errors. In this paper, we present Motion DUSt3R (MonST3R), a novel geometry-first approach that directly estimates per-timestep geometry from dynamic scenes. Our key insight is that by simply estimating a pointmap for each timestep, we can effectively adapt DUST3R's representation, previously only used for static scenes, to dynamic scenes. However, this approach presents a significant challenge: the scarcity of suitable training data, namely dynamic, posed videos with depth labels. Despite this, we show that by posing the problem as a fine-tuning task, identifying several suitable datasets, and strategically training the model on this limited data, we can surprisingly enable the model to handle dynamics, even without an explicit motion representation. Based on this, we introduce new optimizations for several downstream video-specific tasks and demonstrate strong performance on video depth and camera pose estimation, outperforming prior work in terms of robustness and efficiency. Moreover, MonST3R shows promising results for primarily feed-forward 4D reconstruction.

Humans excel at forecasting the future dynamics of a scene given just a single image. Video generation models that can mimic this ability are an essential component for intelligent systems. Recent approaches have improved temporal coherence and 3D consistency in single-image-conditioned video generation. However, these methods often lack robust user controllability, such as modifying the camera path, limiting their applicability in real-world applications. Most existing camera-controlled image-to-video models struggle with accurately modeling camera motion, maintaining temporal consistency, and preserving geometric integrity. Leveraging explicit intermediate 3D representations offers a promising solution by enabling coherent video generation aligned with a given camera trajectory. Although these methods often use 3D point clouds to render scenes and introduce object motion in a later stage, this two-step process still falls short in achieving full temporal consistency, despite allowing precise control over camera movement. We propose a novel framework that constructs a 3D Gaussian scene representation and samples plausible object motion, given a single image in a single forward pass. This enables fast, camera-guided video generation without the need for iterative denoising to inject object motion into render frames. Extensive experiments on the KITTI, Waymo, RealEstate10K and DL3DV-10K datasets demonstrate that our method achieves state-of-the-art video quality and inference efficiency. The project page is available at https://melonienimasha.github.io/Pixel-to-4D-Website.

We propose a new loss function, called motion loss, for the problem of monocular 3D Human pose estimation from 2D pose. In computing motion loss, a simple yet effective representation for keypoint motion, called pairwise motion encoding, is introduced. We design a new graph convolutional network architecture, U-shaped GCN (UGCN). It captures both short-term and long-term motion information to fully leverage the additional supervision from the motion loss. We experiment training UGCN with the motion loss on two large scale benchmarks: Human3.6M and MPI-INF-3DHP. Our model surpasses other state-of-the-art models by a large margin. It also demonstrates strong capacity in producing smooth 3D sequences and recovering keypoint motion.

We present GRAPE (Group RepresentAtional Position Encoding), a unified framework for positional encoding based on group actions. GRAPE brings together two families of mechanisms: (i) multiplicative rotations (Multiplicative GRAPE) in SO(d) and (ii) additive logit biases (Additive GRAPE) arising from unipotent actions in the general linear group GL. In Multiplicative GRAPE, a position n in Z (or t in R) acts as G(n)=exp(n,ω,L) with a rank-2 skew generator L in R^{d times d}, yielding a relative, compositional, norm-preserving map with a closed-form matrix exponential. RoPE is recovered exactly when the d/2 planes are the canonical coordinate pairs with log-uniform spectrum. Learned commuting subspaces and compact non-commuting mixtures strictly extend this geometry to capture cross-subspace feature coupling at O(d) and O(r d) cost per head, respectively. In Additive GRAPE, additive logits arise as rank-1 (or low-rank) unipotent actions, recovering ALiBi and the Forgetting Transformer (FoX) as exact special cases while preserving an exact relative law and streaming cacheability. Altogether, GRAPE supplies a principled design space for positional geometry in long-context models, subsuming RoPE and ALiBi as special cases. Project Page: https://github.com/model-architectures/GRAPE.

We introduce a self-supervised method for learning visual correspondence from unlabeled video. The main idea is to use cycle-consistency in time as free supervisory signal for learning visual representations from scratch. At training time, our model learns a feature map representation to be useful for performing cycle-consistent tracking. At test time, we use the acquired representation to find nearest neighbors across space and time. We demonstrate the generalizability of the representation -- without finetuning -- across a range of visual correspondence tasks, including video object segmentation, keypoint tracking, and optical flow. Our approach outperforms previous self-supervised methods and performs competitively with strongly supervised methods.

We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.

We present a novel self-supervised algorithm named MotionHint for monocular visual odometry (VO) that takes motion constraints into account. A key aspect of our approach is to use an appropriate motion model that can help existing self-supervised monocular VO (SSM-VO) algorithms to overcome issues related to the local minima within their self-supervised loss functions. The motion model is expressed with a neural network named PPnet. It is trained to coarsely predict the next pose of the camera and the uncertainty of this prediction. Our self-supervised approach combines the original loss and the motion loss, which is the weighted difference between the prediction and the generated ego-motion. Taking two existing SSM-VO systems as our baseline, we evaluate our MotionHint algorithm on the standard KITTI benchmark. Experimental results show that our MotionHint algorithm can be easily applied to existing open-sourced state-of-the-art SSM-VO systems to greatly improve the performance by reducing the resulting ATE by up to 28.73%.

Retrieving videos based on semantic motion is a fundamental, yet unsolved, problem. Existing video representation approaches overly rely on static appearance and scene context rather than motion dynamics, a bias inherited from their training data and objectives. Conversely, traditional motion-centric inputs like optical flow lack the semantic grounding needed to understand high-level motion. To demonstrate this inherent bias, we introduce the SimMotion benchmarks, combining controlled synthetic data with a new human-annotated real-world dataset. We show that existing models perform poorly on these benchmarks, often failing to disentangle motion from appearance. To address this gap, we propose SemanticMoments, a simple, training-free method that computes temporal statistics (specifically, higher-order moments) over features from pre-trained semantic models. Across our benchmarks, SemanticMoments consistently outperforms existing RGB, flow, and text-supervised methods. This demonstrates that temporal statistics in a semantic feature space provide a scalable and perceptually grounded foundation for motion-centric video understanding.

Existing methods for human motion control in video generation typically rely on either 2D poses or explicit 3D parametric models (e.g., SMPL) as control signals. However, 2D poses rigidly bind motion to the driving viewpoint, precluding novel-view synthesis. Explicit 3D models, though structurally informative, suffer from inherent inaccuracies (e.g., depth ambiguity and inaccurate dynamics) which, when used as a strong constraint, override the powerful intrinsic 3D awareness of large-scale video generators. In this work, we revisit motion control from a 3D-aware perspective, advocating for an implicit, view-agnostic motion representation that naturally aligns with the generator's spatial priors rather than depending on externally reconstructed constraints. We introduce 3DiMo, which jointly trains a motion encoder with a pretrained video generator to distill driving frames into compact, view-agnostic motion tokens, injected semantically via cross-attention. To foster 3D awareness, we train with view-rich supervision (i.e., single-view, multi-view, and moving-camera videos), forcing motion consistency across diverse viewpoints. Additionally, we use auxiliary geometric supervision that leverages SMPL only for early initialization and is annealed to zero, enabling the model to transition from external 3D guidance to learning genuine 3D spatial motion understanding from the data and the generator's priors. Experiments confirm that 3DiMo faithfully reproduces driving motions with flexible, text-driven camera control, significantly surpassing existing methods in both motion fidelity and visual quality.

Event-based cameras are ideal for line-based motion estimation, since they predominantly respond to edges in the scene. However, accurately determining the camera displacement based on events continues to be an open problem. This is because line feature extraction and dynamics estimation are tightly coupled when using event cameras, and no precise model is currently available for describing the complex structures generated by lines in the space-time volume of events. We solve this problem by deriving the correct non-linear parametrization of such manifolds, which we term eventails, and demonstrate its application to event-based linear motion estimation, with known rotation from an Inertial Measurement Unit. Using this parametrization, we introduce a novel minimal 5-point solver that jointly estimates line parameters and linear camera velocity projections, which can be fused into a single, averaged linear velocity when considering multiple lines. We demonstrate on both synthetic and real data that our solver generates more stable relative motion estimates than other methods while capturing more inliers than clustering based on spatio-temporal planes. In particular, our method consistently achieves a 100% success rate in estimating linear velocity where existing closed-form solvers only achieve between 23% and 70%. The proposed eventails contribute to a better understanding of spatio-temporal event-generated geometries and we thus believe it will become a core building block of future event-based motion estimation algorithms.

We propose a new problem, In-2-4D, for generative 4D (i.e., 3D + motion) inbetweening from a minimalistic input setting: two single-view images capturing an object in two distinct motion states. Given two images representing the start and end states of an object in motion, our goal is to generate and reconstruct the motion in 4D. We utilize a video interpolation model to predict the motion, but large frame-to-frame motions can lead to ambiguous interpretations. To overcome this, we employ a hierarchical approach to identify keyframes that are visually close to the input states and show significant motion, then generate smooth fragments between them. For each fragment, we construct the 3D representation of the keyframe using Gaussian Splatting. The temporal frames within the fragment guide the motion, enabling their transformation into dynamic Gaussians through a deformation field. To improve temporal consistency and refine 3D motion, we expand the self-attention of multi-view diffusion across timesteps and apply rigid transformation regularization. Finally, we merge the independently generated 3D motion segments by interpolating boundary deformation fields and optimizing them to align with the guiding video, ensuring smooth and flicker-free transitions. Through extensive qualitative and quantitiave experiments as well as a user study, we show the effectiveness of our method and its components. The project page is available at https://in-2-4d.github.io/

Recent self-supervised video representation learning methods have found significant success by exploring essential properties of videos, e.g. speed, temporal order, etc. This work exploits an essential yet under-explored property of videos, the video continuity, to obtain supervision signals for self-supervised representation learning. Specifically, we formulate three novel continuity-related pretext tasks, i.e. continuity justification, discontinuity localization, and missing section approximation, that jointly supervise a shared backbone for video representation learning. This self-supervision approach, termed as Continuity Perception Network (CPNet), solves the three tasks altogether and encourages the backbone network to learn local and long-ranged motion and context representations. It outperforms prior arts on multiple downstream tasks, such as action recognition, video retrieval, and action localization. Additionally, the video continuity can be complementary to other coarse-grained video properties for representation learning, and integrating the proposed pretext task to prior arts can yield much performance gains.

Dynamic scene reconstruction is a long-term challenge in the field of 3D vision. Recently, the emergence of 3D Gaussian Splatting has provided new insights into this problem. Although subsequent efforts rapidly extend static 3D Gaussian to dynamic scenes, they often lack explicit constraints on object motion, leading to optimization difficulties and performance degradation. To address the above issues, we propose a novel deformable 3D Gaussian splatting framework called MotionGS, which explores explicit motion priors to guide the deformation of 3D Gaussians. Specifically, we first introduce an optical flow decoupling module that decouples optical flow into camera flow and motion flow, corresponding to camera movement and object motion respectively. Then the motion flow can effectively constrain the deformation of 3D Gaussians, thus simulating the motion of dynamic objects. Additionally, a camera pose refinement module is proposed to alternately optimize 3D Gaussians and camera poses, mitigating the impact of inaccurate camera poses. Extensive experiments in the monocular dynamic scenes validate that MotionGS surpasses state-of-the-art methods and exhibits significant superiority in both qualitative and quantitative results. Project page: https://ruijiezhu94.github.io/MotionGS_page

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data. Most SSL approaches rely on strong, well-established, handcrafted data augmentations to generate diverse views for representation learning. However, designing such augmentations requires domain-specific knowledge and implicitly imposes representational invariances on the model, which can limit generalization. In this work, we propose an unsupervised representation learning method that replaces augmentations by generating views using orthonormal bases and overcomplete frames. We show that embeddings learned from orthonormal and overcomplete spaces reside on distinct manifolds, shaped by the geometric biases introduced by representing samples in different spaces. By jointly leveraging the complementary geometry of these distinct manifolds, our approach achieves superior performance without artificially increasing data diversity through strong augmentations. We demonstrate the effectiveness of our method on nine datasets across five temporal sequence tasks, where signal-specific characteristics make data augmentations particularly challenging. Without relying on augmentation-induced diversity, our method achieves performance gains of up to 15--20\% over existing self-supervised approaches. Source code: https://github.com/eth-siplab/Learning-with-FrameProjections

We introduce Motion2VecSets, a 4D diffusion model for dynamic surface reconstruction from point cloud sequences. While existing state-of-the-art methods have demonstrated success in reconstructing non-rigid objects using neural field representations, conventional feed-forward networks encounter challenges with ambiguous observations from noisy, partial, or sparse point clouds. To address these challenges, we introduce a diffusion model that explicitly learns the shape and motion distribution of non-rigid objects through an iterative denoising process of compressed latent representations. The diffusion-based priors enable more plausible and probabilistic reconstructions when handling ambiguous inputs. We parameterize 4D dynamics with latent sets instead of using global latent codes. This novel 4D representation allows us to learn local shape and deformation patterns, leading to more accurate non-linear motion capture and significantly improving generalizability to unseen motions and identities. For more temporally-coherent object tracking, we synchronously denoise deformation latent sets and exchange information across multiple frames. To avoid computational overhead, we designed an interleaved space and time attention block to alternately aggregate deformation latents along spatial and temporal domains. Extensive comparisons against state-of-the-art methods demonstrate the superiority of our Motion2VecSets in 4D reconstruction from various imperfect observations. More detailed information can be found at https://vveicao.github.io/projects/Motion2VecSets/.

We introduce Temporal Residual Jacobians as a novel representation to enable data-driven motion transfer. Our approach does not assume access to any rigging or intermediate shape keyframes, produces geometrically and temporally consistent motions, and can be used to transfer long motion sequences. Central to our approach are two coupled neural networks that individually predict local geometric and temporal changes that are subsequently integrated, spatially and temporally, to produce the final animated meshes. The two networks are jointly trained, complement each other in producing spatial and temporal signals, and are supervised directly with 3D positional information. During inference, in the absence of keyframes, our method essentially solves a motion extrapolation problem. We test our setup on diverse meshes (synthetic and scanned shapes) to demonstrate its superiority in generating realistic and natural-looking animations on unseen body shapes against SoTA alternatives. Supplemental video and code are available at https://temporaljacobians.github.io/ .

Remarkable advances have been achieved recently in learning neural representations that characterize object geometry, while generating textured objects suitable for downstream applications and 3D rendering remains at an early stage. In particular, reconstructing textured geometry from images of real objects is a significant challenge -- reconstructed geometry is often inexact, making realistic texturing a significant challenge. We present Mesh2Tex, which learns a realistic object texture manifold from uncorrelated collections of 3D object geometry and photorealistic RGB images, by leveraging a hybrid mesh-neural-field texture representation. Our texture representation enables compact encoding of high-resolution textures as a neural field in the barycentric coordinate system of the mesh faces. The learned texture manifold enables effective navigation to generate an object texture for a given 3D object geometry that matches to an input RGB image, which maintains robustness even under challenging real-world scenarios where the mesh geometry approximates an inexact match to the underlying geometry in the RGB image. Mesh2Tex can effectively generate realistic object textures for an object mesh to match real images observations towards digitization of real environments, significantly improving over previous state of the art.

Dynamic objects in our physical 4D (3D + time) world are constantly evolving, deforming, and interacting with other objects, leading to diverse 4D scene dynamics. In this paper, we present a universal generative pipeline, CHORD, for CHOReographing Dynamic objects and scenes and synthesizing this type of phenomena. Traditional rule-based graphics pipelines to create these dynamics are based on category-specific heuristics, yet are labor-intensive and not scalable. Recent learning-based methods typically demand large-scale datasets, which may not cover all object categories in interest. Our approach instead inherits the universality from the video generative models by proposing a distillation-based pipeline to extract the rich Lagrangian motion information hidden in the Eulerian representations of 2D videos. Our method is universal, versatile, and category-agnostic. We demonstrate its effectiveness by conducting experiments to generate a diverse range of multi-body 4D dynamics, show its advantage compared to existing methods, and demonstrate its applicability in generating robotics manipulation policies. Project page: https://yanzhelyu.github.io/chord

This paper addresses the challenge of text-conditioned streaming motion generation, which requires us to predict the next-step human pose based on variable-length historical motions and incoming texts. Existing methods struggle to achieve streaming motion generation, e.g., diffusion models are constrained by pre-defined motion lengths, while GPT-based methods suffer from delayed response and error accumulation problem due to discretized non-causal tokenization. To solve these problems, we propose MotionStreamer, a novel framework that incorporates a continuous causal latent space into a probabilistic autoregressive model. The continuous latents mitigate information loss caused by discretization and effectively reduce error accumulation during long-term autoregressive generation. In addition, by establishing temporal causal dependencies between current and historical motion latents, our model fully utilizes the available information to achieve accurate online motion decoding. Experiments show that our method outperforms existing approaches while offering more applications, including multi-round generation, long-term generation, and dynamic motion composition. Project Page: https://zju3dv.github.io/MotionStreamer/

We present HY-Motion 1.0, a series of state-of-the-art, large-scale, motion generation models capable of generating 3D human motions from textual descriptions. HY-Motion 1.0 represents the first successful attempt to scale up Diffusion Transformer (DiT)-based flow matching models to the billion-parameter scale within the motion generation domain, delivering instruction-following capabilities that significantly outperform current open-source benchmarks. Uniquely, we introduce a comprehensive, full-stage training paradigm -- including large-scale pretraining on over 3,000 hours of motion data, high-quality fine-tuning on 400 hours of curated data, and reinforcement learning from both human feedback and reward models -- to ensure precise alignment with the text instruction and high motion quality. This framework is supported by our meticulous data processing pipeline, which performs rigorous motion cleaning and captioning. Consequently, our model achieves the most extensive coverage, spanning over 200 motion categories across 6 major classes. We release HY-Motion 1.0 to the open-source community to foster future research and accelerate the transition of 3D human motion generation models towards commercial maturity.

Text-to-motion generation is a crucial task in computer vision, which generates the target 3D motion by the given text. The existing annotated datasets are limited in scale, resulting in most existing methods overfitting to the small datasets and unable to generalize to the motions of the open domain. Some methods attempt to solve the open-vocabulary motion generation problem by aligning to the CLIP space or using the Pretrain-then-Finetuning paradigm. However, the current annotated dataset's limited scale only allows them to achieve mapping from sub-text-space to sub-motion-space, instead of mapping between full-text-space and full-motion-space (full mapping), which is the key to attaining open-vocabulary motion generation. To this end, this paper proposes to leverage the atomic motion (simple body part motions over a short time period) as an intermediate representation, and leverage two orderly coupled steps, i.e., Textual Decomposition and Sub-motion-space Scattering, to address the full mapping problem. For Textual Decomposition, we design a fine-grained description conversion algorithm, and combine it with the generalization ability of a large language model to convert any given motion text into atomic texts. Sub-motion-space Scattering learns the compositional process from atomic motions to the target motions, to make the learned sub-motion-space scattered to form the full-motion-space. For a given motion of the open domain, it transforms the extrapolation into interpolation and thereby significantly improves generalization. Our network, DSO-Net, combines textual decomposition and sub-motion-space scattering to solve the open-vocabulary motion generation. Extensive experiments demonstrate that our DSO-Net achieves significant improvements over the state-of-the-art methods on open-vocabulary motion generation. Code is available at https://vankouf.github.io/DSONet/.

3D Reconstruction of moving articulated objects without additional information about object structure is a challenging problem. Current methods overcome such challenges by employing category-specific skeletal models. Consequently, they do not generalize well to articulated objects in the wild. We treat an articulated object as an unknown, semi-rigid skeletal structure surrounded by nonrigid material (e.g., skin). Our method simultaneously estimates the visible (explicit) representation (3D shapes, colors, camera parameters) and the implicit skeletal representation, from motion cues in the object video without 3D supervision. Our implicit representation consists of four parts. (1) Skeleton, which specifies how semi-rigid parts are connected. (2) black{Skinning Weights}, which associates each surface vertex with semi-rigid parts with probability. (3) Rigidity Coefficients, specifying the articulation of the local surface. (4) Time-Varying Transformations, which specify the skeletal motion and surface deformation parameters. We introduce an algorithm that uses physical constraints as regularization terms and iteratively estimates both implicit and explicit representations. Our method is category-agnostic, thus eliminating the need for category-specific skeletons, we show that our method outperforms state-of-the-art across standard video datasets.

Animating images with interactive motion control has garnered popularity for image-to-video (I2V) generation. Modern approaches typically rely on large Gaussian kernels to extend motion trajectories as condition without explicitly defining movement region, leading to coarse motion control and failing to disentangle object and camera moving. To alleviate these, we present MotionPro, a precise motion controller that novelly leverages region-wise trajectory and motion mask to regulate fine-grained motion synthesis and identify target motion category (i.e., object or camera moving), respectively. Technically, MotionPro first estimates the flow maps on each training video via a tracking model, and then samples the region-wise trajectories to simulate inference scenario. Instead of extending flow through large Gaussian kernels, our region-wise trajectory approach enables more precise control by directly utilizing trajectories within local regions, thereby effectively characterizing fine-grained movements. A motion mask is simultaneously derived from the predicted flow maps to capture the holistic motion dynamics of the movement regions. To pursue natural motion control, MotionPro further strengthens video denoising by incorporating both region-wise trajectories and motion mask through feature modulation. More remarkably, we meticulously construct a benchmark, i.e., MC-Bench, with 1.1K user-annotated image-trajectory pairs, for the evaluation of both fine-grained and object-level I2V motion control. Extensive experiments conducted on WebVid-10M and MC-Bench demonstrate the effectiveness of MotionPro. Please refer to our project page for more results: https://zhw-zhang.github.io/MotionPro-page/.

Generating 3D human motion from text descriptions remains challenging due to the diverse and complex nature of human motion. While existing methods excel within the training distribution, they often struggle with out-of-distribution motions, limiting their applicability in real-world scenarios. Existing VQVAE-based methods often fail to represent novel motions faithfully using discrete tokens, which hampers their ability to generalize beyond seen data. Meanwhile, diffusion-based methods operating on continuous representations often lack fine-grained control over individual frames. To address these challenges, we propose a robust motion generation framework MoMADiff, which combines masked modeling with diffusion processes to generate motion using frame-level continuous representations. Our model supports flexible user-provided keyframe specification, enabling precise control over both spatial and temporal aspects of motion synthesis. MoMADiff demonstrates strong generalization capability on novel text-to-motion datasets with sparse keyframes as motion prompts. Extensive experiments on two held-out datasets and two standard benchmarks show that our method consistently outperforms state-of-the-art models in motion quality, instruction fidelity, and keyframe adherence. The code is available at: https://github.com/zzysteve/MoMADiff

Temporal motion modeling has always been a key component in multiple object tracking (MOT) which can ensure smooth trajectory movement and provide accurate positional information to enhance association precision. However, current motion models struggle to be both efficient and effective across different application scenarios. To this end, we propose TrackSSM inspired by the recently popular state space models (SSM), a unified encoder-decoder motion framework that uses data-dependent state space model to perform temporal motion of trajectories. Specifically, we propose Flow-SSM, a module that utilizes the position and motion information from historical trajectories to guide the temporal state transition of object bounding boxes. Based on Flow-SSM, we design a flow decoder. It is composed of a cascaded motion decoding module employing Flow-SSM, which can use the encoded flow information to complete the temporal position prediction of trajectories. Additionally, we propose a Step-by-Step Linear (S^2L) training strategy. By performing linear interpolation between the positions of the object in the previous frame and the current frame, we construct the pseudo labels of step-by-step linear training, ensuring that the trajectory flow information can better guide the object bounding box in completing temporal transitions. TrackSSM utilizes a simple Mamba-Block to build a motion encoder for historical trajectories, forming a temporal motion model with an encoder-decoder structure in conjunction with the flow decoder. TrackSSM is applicable to various tracking scenarios and achieves excellent tracking performance across multiple benchmarks, further extending the potential of SSM-like temporal motion models in multi-object tracking tasks. Code and models are publicly available at https://github.com/Xavier-Lin/TrackSSM.

Generating human motion with precise spatial control is a challenging problem. Existing approaches often require task-specific training or slow optimization, and enforcing hard constraints frequently disrupts motion naturalness. Building on the observation that many animation tasks can be formulated as a linear inverse problem, we introduce ProjFlow, a training-free sampler that achieves zero-shot, exact satisfaction of linear spatial constraints while preserving motion realism. Our key advance is a novel kinematics-aware metric that encodes skeletal topology. This metric allows the sampler to enforce hard constraints by distributing corrections coherently across the entire skeleton, avoiding the unnatural artifacts of naive projection. Furthermore, for sparse inputs, such as filling in long gaps between a few keyframes, we introduce a time-varying formulation using pseudo-observations that fade during sampling. Extensive experiments on representative applications, motion inpainting, and 2D-to-3D lifting, demonstrate that ProjFlow achieves exact constraint satisfaction and matches or improves realism over zero-shot baselines, while remaining competitive with training-based controllers.

We present a method that simultaneously addresses the tasks of dynamic scene novel-view synthesis and six degree-of-freedom (6-DOF) tracking of all dense scene elements. We follow an analysis-by-synthesis framework, inspired by recent work that models scenes as a collection of 3D Gaussians which are optimized to reconstruct input images via differentiable rendering. To model dynamic scenes, we allow Gaussians to move and rotate over time while enforcing that they have persistent color, opacity, and size. By regularizing Gaussians' motion and rotation with local-rigidity constraints, we show that our Dynamic 3D Gaussians correctly model the same area of physical space over time, including the rotation of that space. Dense 6-DOF tracking and dynamic reconstruction emerges naturally from persistent dynamic view synthesis, without requiring any correspondence or flow as input. We demonstrate a large number of downstream applications enabled by our representation, including first-person view synthesis, dynamic compositional scene synthesis, and 4D video editing.

Action Quality Assessment (AQA) evaluates diverse skills but models struggle with non-stationary data. We propose Continual AQA (CAQA) to refine models using sparse new data. Feature replay preserves memory without storing raw inputs. However, the misalignment between static old features and the dynamically changing feature manifold causes severe catastrophic forgetting. To address this novel problem, we propose Manifold-Aligned Graph Regularization (MAGR), which first aligns deviated old features to the current feature manifold, ensuring representation consistency. It then constructs a graph jointly arranging old and new features aligned with quality scores. Experiments show MAGR outperforms recent strong baselines with up to 6.56%, 5.66%, 15.64%, and 9.05% correlation gains on the MTL-AQA, FineDiving, UNLV-Dive, and JDM-MSA split datasets, respectively. This validates MAGR for continual assessment challenges arising from non-stationary skill variations.

Motion understanding is fundamental to physical reasoning, enabling models to infer dynamics and predict future states. However, state-of-the-art models still struggle on recent motion benchmarks, primarily due to the scarcity of large-scale, fine-grained motion datasets. Existing motion datasets are often constructed from costly manual annotation, severely limiting scalability. To address this challenge, we introduce FoundationMotion, a fully automated data curation pipeline that constructs large-scale motion datasets. Our approach first detects and tracks objects in videos to extract their trajectories, then leverages these trajectories and video frames with Large Language Models (LLMs) to generate fine-grained captions and diverse question-answer pairs about motion and spatial reasoning. Using datasets produced by this pipeline, we fine-tune open-source models including NVILA-Video-15B and Qwen2.5-7B, achieving substantial improvements in motion understanding without compromising performance on other tasks. Notably, our models outperform strong closed-source baselines like Gemini-2.5 Flash and large open-source models such as Qwen2.5-VL-72B across diverse motion understanding datasets and benchmarks. FoundationMotion thus provides a scalable solution for curating fine-grained motion datasets that enable effective fine-tuning of diverse models to enhance motion understanding and spatial reasoning capabilities.

We present a unified representation for actionable spatial perception: 3D Dynamic Scene Graphs. Scene graphs are directed graphs where nodes represent entities in the scene (e.g. objects, walls, rooms), and edges represent relations (e.g. inclusion, adjacency) among nodes. Dynamic scene graphs (DSGs) extend this notion to represent dynamic scenes with moving agents (e.g. humans, robots), and to include actionable information that supports planning and decision-making (e.g. spatio-temporal relations, topology at different levels of abstraction). Our second contribution is to provide the first fully automatic Spatial PerceptIon eNgine(SPIN) to build a DSG from visual-inertial data. We integrate state-of-the-art techniques for object and human detection and pose estimation, and we describe how to robustly infer object, robot, and human nodes in crowded scenes. To the best of our knowledge, this is the first paper that reconciles visual-inertial SLAM and dense human mesh tracking. Moreover, we provide algorithms to obtain hierarchical representations of indoor environments (e.g. places, structures, rooms) and their relations. Our third contribution is to demonstrate the proposed spatial perception engine in a photo-realistic Unity-based simulator, where we assess its robustness and expressiveness. Finally, we discuss the implications of our proposal on modern robotics applications. 3D Dynamic Scene Graphs can have a profound impact on planning and decision-making, human-robot interaction, long-term autonomy, and scene prediction. A video abstract is available at https://youtu.be/SWbofjhyPzI

Efficient neural representations for dynamic video scenes are critical for applications ranging from video compression to interactive simulations. Yet, existing methods often face challenges related to high memory usage, lengthy training times, and temporal consistency. To address these issues, we introduce a novel neural video representation that combines 3D Gaussian splatting with continuous camera motion modeling. By leveraging Neural ODEs, our approach learns smooth camera trajectories while maintaining an explicit 3D scene representation through Gaussians. Additionally, we introduce a spatiotemporal hierarchical learning strategy, progressively refining spatial and temporal features to enhance reconstruction quality and accelerate convergence. This memory-efficient approach achieves high-quality rendering at impressive speeds. Experimental results show that our hierarchical learning, combined with robust camera motion modeling, captures complex dynamic scenes with strong temporal consistency, achieving state-of-the-art performance across diverse video datasets in both high- and low-motion scenarios.

We present MovingParts, a NeRF-based method for dynamic scene reconstruction and part discovery. We consider motion as an important cue for identifying parts, that all particles on the same part share the common motion pattern. From the perspective of fluid simulation, existing deformation-based methods for dynamic NeRF can be seen as parameterizing the scene motion under the Eulerian view, i.e., focusing on specific locations in space through which the fluid flows as time passes. However, it is intractable to extract the motion of constituting objects or parts using the Eulerian view representation. In this work, we introduce the dual Lagrangian view and enforce representations under the Eulerian/Lagrangian views to be cycle-consistent. Under the Lagrangian view, we parameterize the scene motion by tracking the trajectory of particles on objects. The Lagrangian view makes it convenient to discover parts by factorizing the scene motion as a composition of part-level rigid motions. Experimentally, our method can achieve fast and high-quality dynamic scene reconstruction from even a single moving camera, and the induced part-based representation allows direct applications of part tracking, animation, 3D scene editing, etc.

Novel view synthesis from an in-the-wild video is difficult due to challenges like scene dynamics and lack of parallax. While existing methods have shown promising results with implicit neural radiance fields, they are slow to train and render. This paper revisits explicit video representations to synthesize high-quality novel views from a monocular video efficiently. We treat static and dynamic video content separately. Specifically, we build a global static scene model using an extended plane-based scene representation to synthesize temporally coherent novel video. Our plane-based scene representation is augmented with spherical harmonics and displacement maps to capture view-dependent effects and model non-planar complex surface geometry. We opt to represent the dynamic content as per-frame point clouds for efficiency. While such representations are inconsistency-prone, minor temporal inconsistencies are perceptually masked due to motion. We develop a method to quickly estimate such a hybrid video representation and render novel views in real time. Our experiments show that our method can render high-quality novel views from an in-the-wild video with comparable quality to state-of-the-art methods while being 100x faster in training and enabling real-time rendering.

Motion magnification helps us visualize subtle, imperceptible motion. However, prior methods only work for 2D videos captured with a fixed camera. We present a 3D motion magnification method that can magnify subtle motions from scenes captured by a moving camera, while supporting novel view rendering. We represent the scene with time-varying radiance fields and leverage the Eulerian principle for motion magnification to extract and amplify the variation of the embedding of a fixed point over time. We study and validate our proposed principle for 3D motion magnification using both implicit and tri-plane-based radiance fields as our underlying 3D scene representation. We evaluate the effectiveness of our method on both synthetic and real-world scenes captured under various camera setups.